Metrics
Report explains how the response categories from NLSY97 questionnaire are labeled and demonstrates application of labeled factors in data operations and graphing.
Sections:
1. Labeling Factor Levels
2. Age-Period-Cohort structure
3. Mapping Church Attendance
4. Selecting & Augmenting datasets for modeling
Data In
Initial point of departure - the databox of the selected sample, described in the Methods chapter. 
This databox corresponds to the dataset dsL produced by Derive_dsL_from_Extract report.
dsL<-readRDS("./Data/Derived/dsL.rds")<
1. Labeling Factor Levels
Review of the item reference cards shows that initially, all items were recorded on some discrete scale, either counting occasions or assigning an intiger to a category of response. However, in the original dataset they are recorded as either a numerical value or an intiger
str(dsL)'data.frame': 134760 obs. of 60 variables:
$ sample : int 1 1 1 1 1 1 1 1 1 1 ...
$ id : int 1 1 1 1 1 1 1 1 1 1 ...
$ sex : int 2 2 2 2 2 2 2 2 2 2 ...
$ race : int 4 4 4 4 4 4 4 4 4 4 ...
$ bmonth : int 9 9 9 9 9 9 9 9 9 9 ...
$ byear : int 1981 1981 1981 1981 1981 1981 1981 1981 1981 1981 ...
$ attendPR : int 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ year : int 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 ...
$ agemon : num 190 206 219 231 243 256 266 279 290 302 ...
$ ageyear : num 15 17 18 19 20 21 22 23 24 25 ...
$ famrel : num NA NA NA NA NA NA NA NA NA NA ...
$ attend : num NA NA NA 1 6 2 1 1 1 1 ...
$ values : num NA NA NA NA NA 1 NA NA 0 NA ...
$ todo : num NA NA NA NA NA 1 NA NA 1 NA ...
$ obeyed : num NA NA NA NA NA 1 NA NA 0 NA ...
$ pray : num NA NA NA NA NA 0 NA NA 0 NA ...
$ decisions : num NA NA NA NA NA 1 NA NA 1 NA ...
$ relpref : num NA NA NA NA NA NA NA NA 21 NA ...
$ bornagain : num NA NA NA NA NA NA NA NA NA NA ...
$ faith : num NA NA NA NA NA NA NA NA NA NA ...
$ calm : num NA NA NA 3 NA 4 NA 4 NA 4 ...
$ blue : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ happy : num NA NA NA 3 NA 3 NA 4 NA 4 ...
$ depressed : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ nervous : num NA NA NA 3 NA 1 NA 1 NA 1 ...
$ tv : num NA NA NA NA NA 2 NA NA NA NA ...
$ computer : num NA NA NA NA NA 5 NA NA NA NA ...
$ internet : num NA NA NA NA NA NA 1 0 1 1 ...
$ sampleF : Ord.factor w/ 2 levels "Cross-Sectional"<..: 1 1 1 1 1 1 1 1 1 1 ...
$ idF : Factor w/ 8984 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
$ sexF : Ord.factor w/ 3 levels "Male"<"Female"<..: 2 2 2 2 2 2 2 2 2 2 ...
$ raceF : Ord.factor w/ 4 levels "Black"<"Hispanic"<..: NA NA NA NA NA NA NA NA NA NA ...
$ bmonthF : Ord.factor w/ 12 levels "Jan"<"Feb"<"Mar"<..: 9 9 9 9 9 9 9 9 9 9 ...
$ byearF : Factor w/ 5 levels "1980","1981",..: 2 2 2 2 2 2 2 2 2 2 ...
$ attendPRF : Ord.factor w/ 8 levels "Never"<"Once or Twice"<..: 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPRF : Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPRF: Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: 21 21 21 21 21 21 21 21 21 21 ...
$ yearF : Factor w/ 15 levels "1997","1998",..: 1 2 3 4 5 6 7 8 9 10 ...
$ agemonF : Factor w/ 244 levels "146","147","148",..: 45 61 74 86 98 111 121 134 145 157 ...
$ ageyearF : Factor w/ 21 levels "12","13","14",..: 4 6 7 8 9 10 11 12 13 14 ...
$ famrelF : Factor w/ 8 levels "0","1","2","3",..: NA NA NA NA NA NA NA NA NA NA ...
$ attendF : Ord.factor w/ 8 levels "Never"<"Once or Twice"<..: NA NA NA 1 6 2 1 1 1 1 ...
$ valuesF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 1 NA ...
$ todoF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 2 NA ...
$ obeyedF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 1 NA ...
$ prayF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 1 NA NA 1 NA ...
$ decisionsF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 2 NA ...
$ relprefF : Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: NA NA NA NA NA NA NA NA 21 NA ...
$ bornagainF : Ord.factor w/ 2 levels "NO"<"YES": NA NA NA NA NA NA NA NA NA NA ...
$ faithF : Ord.factor w/ 5 levels "Exrtemely"<"Very"<..: NA NA NA NA NA NA NA NA NA NA ...
$ calmF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ blueF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ happyF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ depressedF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ nervousF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ tvF : Ord.factor w/ 6 levels "less than 2"<..: NA NA NA NA NA 2 NA NA NA NA ...
$ computerF : Ord.factor w/ 6 levels "None"<"less than 1"<..: NA NA NA NA NA 5 NA NA NA NA ...
$ internetF : Ord.factor w/ 2 levels "No"<"Yes": NA NA NA NA NA NA 2 1 2 2 ...For estimations routines such as lm4 or graphing functions such as ggplot, the data type (string,numeric, factor) is a meaningful input, so a quick access to both formats frequently proves to be convenience. Instead of replacing the initial variables with factors, we’ll create parallel set of variables. The script at the end of LabelingFactorLevels augments the initial dataset dsL with copy of initial variables saved as labeled factors.
str(dsL)'data.frame': 134760 obs. of 60 variables:
$ sample : int 1 1 1 1 1 1 1 1 1 1 ...
$ id : int 1 1 1 1 1 1 1 1 1 1 ...
$ sex : int 2 2 2 2 2 2 2 2 2 2 ...
$ race : int 4 4 4 4 4 4 4 4 4 4 ...
$ bmonth : int 9 9 9 9 9 9 9 9 9 9 ...
$ byear : int 1981 1981 1981 1981 1981 1981 1981 1981 1981 1981 ...
$ attendPR : int 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ year : int 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 ...
$ agemon : num 190 206 219 231 243 256 266 279 290 302 ...
$ ageyear : num 15 17 18 19 20 21 22 23 24 25 ...
$ famrel : num NA NA NA NA NA NA NA NA NA NA ...
$ attend : num NA NA NA 1 6 2 1 1 1 1 ...
$ values : num NA NA NA NA NA 1 NA NA 0 NA ...
$ todo : num NA NA NA NA NA 1 NA NA 1 NA ...
$ obeyed : num NA NA NA NA NA 1 NA NA 0 NA ...
$ pray : num NA NA NA NA NA 0 NA NA 0 NA ...
$ decisions : num NA NA NA NA NA 1 NA NA 1 NA ...
$ relpref : num NA NA NA NA NA NA NA NA 21 NA ...
$ bornagain : num NA NA NA NA NA NA NA NA NA NA ...
$ faith : num NA NA NA NA NA NA NA NA NA NA ...
$ calm : num NA NA NA 3 NA 4 NA 4 NA 4 ...
$ blue : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ happy : num NA NA NA 3 NA 3 NA 4 NA 4 ...
$ depressed : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ nervous : num NA NA NA 3 NA 1 NA 1 NA 1 ...
$ tv : num NA NA NA NA NA 2 NA NA NA NA ...
$ computer : num NA NA NA NA NA 5 NA NA NA NA ...
$ internet : num NA NA NA NA NA NA 1 0 1 1 ...
$ sampleF : Ord.factor w/ 2 levels "Cross-Sectional"<..: 1 1 1 1 1 1 1 1 1 1 ...
$ idF : Factor w/ 8984 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
$ sexF : Ord.factor w/ 3 levels "Male"<"Female"<..: 2 2 2 2 2 2 2 2 2 2 ...
$ raceF : Ord.factor w/ 4 levels "Black"<"Hispanic"<..: NA NA NA NA NA NA NA NA NA NA ...
$ bmonthF : Ord.factor w/ 12 levels "Jan"<"Feb"<"Mar"<..: 9 9 9 9 9 9 9 9 9 9 ...
$ byearF : Factor w/ 5 levels "1980","1981",..: 2 2 2 2 2 2 2 2 2 2 ...
$ attendPRF : Ord.factor w/ 8 levels "Never"<"Once or Twice"<..: 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPRF : Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPRF: Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: 21 21 21 21 21 21 21 21 21 21 ...
$ yearF : Factor w/ 15 levels "1997","1998",..: 1 2 3 4 5 6 7 8 9 10 ...
$ agemonF : Factor w/ 244 levels "146","147","148",..: 45 61 74 86 98 111 121 134 145 157 ...
$ ageyearF : Factor w/ 21 levels "12","13","14",..: 4 6 7 8 9 10 11 12 13 14 ...
$ famrelF : Factor w/ 8 levels "0","1","2","3",..: NA NA NA NA NA NA NA NA NA NA ...
$ attendF : Ord.factor w/ 8 levels "Never"<"Once or Twice"<..: NA NA NA 1 6 2 1 1 1 1 ...
$ valuesF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 1 NA ...
$ todoF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 2 NA ...
$ obeyedF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 1 NA ...
$ prayF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 1 NA NA 1 NA ...
$ decisionsF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 2 NA ...
$ relprefF : Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: NA NA NA NA NA NA NA NA 21 NA ...
$ bornagainF : Ord.factor w/ 2 levels "NO"<"YES": NA NA NA NA NA NA NA NA NA NA ...
$ faithF : Ord.factor w/ 5 levels "Exrtemely"<"Very"<..: NA NA NA NA NA NA NA NA NA NA ...
$ calmF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ blueF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ happyF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ depressedF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ nervousF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ tvF : Ord.factor w/ 6 levels "less than 2"<..: NA NA NA NA NA 2 NA NA NA NA ...
$ computerF : Ord.factor w/ 6 levels "None"<"less than 1"<..: NA NA NA NA NA 5 NA NA NA NA ...
$ internetF : Ord.factor w/ 2 levels "No"<"Yes": NA NA NA NA NA NA 2 1 2 2 ...This give a certain flexibiity to assemble needed dataset quickly and have access to factor labels.
selectCols<-c("year","id","byear","attend","attendF") # type in variable name
ds<-dsL[,selectCols] # select all rows and only columns listed in the object selectCols
print(ds[ds$id==1,]) # print all availible data for respondent with ID number of 1 year id byear attend attendF
1 1997 1 1981 NA <NA>
2 1998 1 1981 NA <NA>
3 1999 1 1981 NA <NA>
4 2000 1 1981 1 Never
5 2001 1 1981 6 About once/week
6 2002 1 1981 2 Once or Twice
7 2003 1 1981 1 Never
8 2004 1 1981 1 Never
9 2005 1 1981 1 Never
10 2006 1 1981 1 Never
11 2007 1 1981 1 Never
12 2008 1 1981 1 Never
13 2009 1 1981 1 Never
14 2010 1 1981 1 Never
15 2011 1 1981 1 NeverHaving quick access to factor labels will come especially handy during graph production.
2. Time metrics : Age, Period, Cohort
NLSY97 sample includes individuals from five cohorts, born between 1980 and 1984.The following graphics shows how birth cohort, age of respondents, and round of observation are related in NSLY97. 
There are several indicators of age in NSLY97 that vary in precision. Birth cohort is the most general one, it was recorded once. Two variables were recorded at each interview: age at the time of the interview in months (agemon) and years (ageyear). Those are not derivatives of each other, but, understandably, are closely related. The variable ageyear records the full number of years a respondent reached at the time of the interview. Due to difficulties of administering the survey, time intervals between the waves could differ.
ds<-dsL[dsL$year %in% c(2000:2011),c('id',"byear","year","attend","ageyear","agemon")]
ds<- ds[ds$id %in% c(25),]
ds$age<-ds$year-ds$byear
ds$ageALT<- ds$agemon/12
print(ds) id byear year attend ageyear agemon age ageALT
364 25 1983 2000 5 17 214 17 17.83
365 25 1983 2001 7 18 226 18 18.83
366 25 1983 2002 7 19 236 19 19.67
367 25 1983 2003 2 21 254 20 21.17
368 25 1983 2004 7 21 261 21 21.75
369 25 1983 2005 5 22 272 22 22.67
370 25 1983 2006 7 23 284 23 23.67
371 25 1983 2007 5 24 295 24 24.58
372 25 1983 2008 7 25 307 25 25.58
373 25 1983 2009 7 26 319 26 26.58
374 25 1983 2010 7 27 332 27 27.67
375 25 1983 2011 7 28 342 28 28.50For example, for one person id=25 the age was recorded as 21 years for both 2003 and 2004 (see ageyear). However, when you examine age in months (agemon) you can see this is rounding issue that disappears once a more precise scale is used. To avoid this potentially confusing peculiarity, age in years will be either calculated as computed as (age = year - byear) or as (ageALT = agemon/12).
3. Mapping Church Attendance
The focal variable of interest is attend, an item measuring church attendance in the current year. Although it was recorded on ordinal scale, 
its resolution allows us to treat it as continuous for the purpose of fitting statistical models.
ds<-(subset(dsL, year==2000)) # only for year 2000
summary(as.numeric(ds$attend)) # summarize as continuous variable Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
1.0 1.0 3.0 3.4 6.0 8.0 965 The basic dataset contains personal identifyer (id), birth year which is also used as cohort indicator (byear), wave of measurement (year) and the focal variable of interest - worship attendance (attend).
id byear year attend attendF
691 47 1982 1997 NA <NA>
692 47 1982 1998 NA <NA>
693 47 1982 1999 NA <NA>
694 47 1982 2000 5 About twice/month
695 47 1982 2001 2 Once or Twice
696 47 1982 2002 4 About once/month
697 47 1982 2003 2 Once or Twice
698 47 1982 2004 3 Less than once/month
699 47 1982 2005 2 Once or Twice
700 47 1982 2006 2 Once or Twice
701 47 1982 2007 3 Less than once/month
702 47 1982 2008 2 Once or Twice
703 47 1982 2009 1 Never
704 47 1982 2010 1 Never
705 47 1982 2011 1 NeverThe view lists all the data for a single subjust (id=1). There are
8984subjects in total.
We have data on attendance for 12 years, from 2000 to 2011. Figure 2 gives a cross-sectional frequency distribution of the data across the years. #### Figure 2. Relative frequency of responses for each observed wave 
Modeling how the frequencies of endorsing particular response item will be the focus of Markov model, which renders well in cross-sectional representations. However, LCM and GMM work with longitudinal data, modeling the trajectory of each individual. The trajectories of subjects with ids of 4, 25, 35, and 47 are plotted in the next graph
Warning: Removed 12 rows containing missing values (geom_path).
Warning: Removed 12 rows containing missing values (geom_point).
The respondent id=35 reported attending no worship services in any of the years, while respodent id=25 seemed to frequent it, indicating weekly attendance in 8 out of the 12 years. Individual id=47 started as a fairly regular attendee of religious services in 2000 (5= “about twice a month”), then gradually declined his involvement to nill in 2009 and on. Respondent id=4, on the other hand started off with a rather passive involvement, reporting attended church only “Once or twice” in 2000, maintained a low level of participation throughout the years, only to surge his attendance in 2011. Each of these trajectories imply a story, a life scenario. Why one person grows in his religious involvement, while other declines, or never develops an interest in the first place? Latent curve models will describe intraindividual trajectories of change, while summarizinig the interindividual similarities and trends.
Previous research in religiousity indicated that age might be one of the primary factors explaining interindividual differences in church attendance. To examine the role of age, we change the metric of time from waves of measurement, as in the previous graph, to biological age.
Warning: Removed 12 rows containing missing values (geom_path).
Warning: Removed 12 rows containing missing values (geom_point).
Persons id=35 and id=25 are peers, in 2000 they were both 17. Respondent id=47 is a year older, in 2000 he was 18. The oldest is id=4, who by the last round of measurement in 2011 is 30 years of age. Perhaps, his increased church attendance could be explained by starting a family of his own?
(ASIDE NOTE: this figure reveals an important detail about the NLSY97 data. The variable ageyear records the full number of years a respondent reached at the time of the interview. Due to difficulties of administering the survey, time intervals between the waves could differ. For example, for person id=25 the age was recorded as 21 years for both 2003 and 2004. However, when you examine age in months (agemon) you can see this is rounding issue that disappears once a more precise scale is used. To avoid this potentially confusing peculiarity, age in years will be either calculated as computed as (age = year - byear) or as (ageALT = agemon/12).
ds<- dsL[dsL$year %in% c(2000:2011),c('id',"byear","year","attend","ageyear","agemon")]
ds<- ds[ds$id %in% c(25),]
ds$age<-ds$year-ds$byear
ds$ageALT<- ds$agemon/12
print(ds) id byear year attend ageyear agemon age ageALT
364 25 1983 2000 5 17 214 17 17.83
365 25 1983 2001 7 18 226 18 18.83
366 25 1983 2002 7 19 236 19 19.67
367 25 1983 2003 2 21 254 20 21.17
368 25 1983 2004 7 21 261 21 21.75
369 25 1983 2005 5 22 272 22 22.67
370 25 1983 2006 7 23 284 23 23.67
371 25 1983 2007 5 24 295 24 24.58
372 25 1983 2008 7 25 307 25 25.58
373 25 1983 2009 7 26 319 26 26.58
374 25 1983 2010 7 27 332 27 27.67
375 25 1983 2011 7 28 342 28 28.504. Selecting and Augmenting data for modeling
We need only a few variables at any given moment in the process of modeling, so let’s select only those we need to describe how respondents’ church attendance was changing across time and age. Let’s start with picking person’s id, wave of measurement, and church attendance
print (dsL[dsL$id==1,c("id","year","attend")]) id year attend
1 1 1997 NA
2 1 1998 NA
3 1 1999 NA
4 1 2000 1
5 1 2001 6
6 1 2002 2
7 1 2003 1
8 1 2004 1
9 1 2005 1
10 1 2006 1
11 1 2007 1
12 1 2008 1
13 1 2009 1
14 1 2010 1
15 1 2011 1Now, let’s add to the selection person’s year of birth and age in months at the time of the interview
selectCols<-c("year","id","byear","agemon","attend") # type in variable name
ds<-dsL[,selectCols] # select all rows and only columns listed in the object selectCols
print(ds[ds$id==1,]) # print all availible data for respondent with ID number of 1 year id byear agemon attend
1 1997 1 1981 190 NA
2 1998 1 1981 206 NA
3 1999 1 1981 219 NA
4 2000 1 1981 231 1
5 2001 1 1981 243 6
6 2002 1 1981 256 2
7 2003 1 1981 266 1
8 2004 1 1981 279 1
9 2005 1 1981 290 1
10 2006 1 1981 302 1
11 2007 1 1981 313 1
12 2008 1 1981 325 1
13 2009 1 1981 337 1
14 2010 1 1981 350 1
15 2011 1 1981 360 1Generally we can select any desired dataset by formula dataset[ condition for rows , condition for columns ]
ds<-dsL[dsL$year %in% c(2000:2011),c('id',"byear","year","attendF","ageyearF","agemon")]
print(ds[ds$id==1,]) id byear year attendF ageyearF agemon
4 1 1981 2000 Never 19 231
5 1 1981 2001 About once/week 20 243
6 1 1981 2002 Once or Twice 21 256
7 1 1981 2003 Never 22 266
8 1 1981 2004 Never 23 279
9 1 1981 2005 Never 24 290
10 1 1981 2006 Never 25 302
11 1 1981 2007 Never 26 313
12 1 1981 2008 Never 27 325
13 1 1981 2009 Never 28 337
14 1 1981 2010 Never 29 350
15 1 1981 2011 Never 29 360